Spectral representation of the particle production out of equilibrium—Schwinger mechanism in pulsed electric fields

Fukushima, Kenji

doi:10.1088/1367-2630/16/7/073031

Cited by 5 publications

(11 citation statements)

References 36 publications

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“…Another physically interesting formalism to describe particle production at intermediate times is to define the timedependent adiabatic particle number through the use of Spectral Functions [58,59], which are constructed in terms of correlation functions of the time-dependent creation and annihilation operators (19) used in (25). In this Section we show how the basis dependence arises in this formalism.…”

Section: Spectral Function Approach To Adiabatic Particle Numbermentioning

confidence: 99%

“…, and the projection onto a set of reference modes, characterized by Q k (t) in (24). In [58,59] a particular basis choice was made, W k = ω k and V k = 0, corresponding to a leading-order adiabatic expansion and a particular phase choice via V k . (45) makes it clear that this is just one of an infinite set of possible choices, for which the final particle number at late asymptotic time is always the same, but for which the particle number at intermediate times can be very different.…”

Section: Spectral Function Approach To Adiabatic Particle Numbermentioning

confidence: 99%

“…In this paper, we examine the truncation of the adiabatic expansion using several common (and equivalent) formulations of particle production: the Bogoliubov [15,39,40,42], Riccati [57], Spectral Function [58,59] and Schrödinger [19,21] approaches. The analysis also extends straightforwardly to the quantum kinetic approach [42][43][44][45][46], and the Dirac-Heisenberg-Wigner approach with time-dependent background fields [48,49].…”

Section: Introductionmentioning

confidence: 99%

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Time dependence of adiabatic particle number

2016

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We consider quantum field theoretic systems subject to a time-dependent perturbation, and discuss the question of defining a time dependent particle number not just at asymptotic early and late times, but also during the perturbation. Naïvely, this is not a well-defined notion for such a non-equilibrium process, as the particle number at intermediate times depends on a basis choice of reference states with respect to which particles and anti-particles are defined, even though the final late-time particle number is independent of this basis choice. The basis choice is associated with a particular truncation of the adiabatic expansion. The adiabatic expansion is divergent, and we show that if this divergent expansion is truncated at its optimal order, a universal time dependence is obtained, confirming a general result of Dingle and Berry. This optimally truncated particle number provides a clear picture of quantum interference effects for perturbations with non-trivial temporal sub-structure. We illustrate these results using several equivalent definitions of adiabatic particle number: the Bogoliubov, Riccati, Spectral Function and Schrödinger picture approaches. In each approach, the particle number may be expressed in terms of the tiny deviations between the exact and adiabatic solutions of the Ermakov-Milne equation for the associated time-dependent oscillators.

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Section: Spectral Function Approach To Adiabatic Particle Numbermentioning

confidence: 99%

Section: Spectral Function Approach To Adiabatic Particle Numbermentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Time dependence of adiabatic particle number

2016

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“…Another extension would be to consider initial states with thermal fermions in addition to thermal photons. Then at O(α 0 ) one has the effect considered in [24,33,35,36,40,47], which leads to a suppression (for fermions) because of the Pauli principle. At O(α 2 ) we would for example have thermal trident pair production, where a thermal fermion interacts with the electromagnetic background field and emits an intermediate photon which subsequently decays into an electron-positron pair.…”

Section: Discussionmentioning

confidence: 99%

“…However, if one takes into account thermal fermions then the Pauli principle leads to a reduction of O(α 0 )[24,33,35,36,40,47].…”

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confidence: 99%

Thermally versus dynamically assisted Schwinger pair production

Torgrimsson

2019

Phys. Rev. D

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We study electron-positron pair production by the combination of a strong, constant electric field and a thermal background. We show that this process is similar to dynamically assisted Schwinger pair production, where the strong field is instead assisted by another coherent field, which is weaker but faster. We treat the interaction with the photons from the thermal background perturbatively, while the interaction with the electric field is nonperturbative (i.e. a Furry picture expansion in α). At O(α 2 ) we have ordinary perturbative Breit-Wheeler pair production assisted nonperturbatively by the electric field. Already at this order we recover the same exponential part of the probability as previous studies, which did not expand in α. This means that we do not have to consider higher orders, so our approach allows us to calculate the pre-exponential part of the probability, which has not been obtained before in this regime. Although the prefactor is in general subdominant compared to the exponential part, in this case it can be important because it scales as α 2 1 and is therefore much smaller than the prefactor at O(α 0 ) (pure Schwinger pair production). We show that, because of the exponential enhancement, O(α 2 ) still gives the dominant contribution for temperatures above a certain threshold, but, because of the small prefactor, the threshold is higher than what the exponential alone would suggest.

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Evolution to the quark–gluon plasma

Fukushima

2016

Rep. Prog. Phys.

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Theoretical studies on the early-time dynamics in the ultra-relativistic heavy-ion collisions are reviewed, including pedagogical introductions on the initial condition with small-[Formula: see text] gluons treated as a color glass condensate, the bottom-up thermalization scenario, plasma/glasma instabilities, basics of some formulations such as the kinetic equations and the classical statistical simulation. More detailed discussions follow to make an overview of recent developments on the fast isotropization, the onset of hydrodynamics, and the transient behavior of momentum spectral cascades.

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Spectral representation of the particle production out of equilibrium—Schwinger mechanism in pulsed electric fields

Cited by 5 publications

References 36 publications

Time dependence of adiabatic particle number

Time dependence of adiabatic particle number

Thermally versus dynamically assisted Schwinger pair production

Evolution to the quark–gluon plasma

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